How large does the photovoltaic system need to be?

Ok, sounds logical, but how much does an inverter cost? Apart from the additional space in the technical room, which I might not have...

Is there perhaps a misunderstanding here that you think you can do without the inverter by using power optimizers!? Unfortunately, you are mistaken and have misunderstood something :(

Edit: ah, obviously I misunderstood you and you mean "an additional/second" inverter.... Sorry.

Four roof sides on an inverter is usually not a problem. It only requires two sides with the same number of modules. Optimizers are only needed if, for example, you want to integrate a dormer with two times two modules each of different orientation. Or with four roof sides where two are heavily (and differently) shaded.

Optimizers only in emergencies. Double the number of plug connections and countless electronic components exposed to moisture and enormous temperature fluctuations.

When these things were developed, it might have been a good idea since there were hardly any inverters with shade management back then. Meanwhile, however, this is standard and every inverter can handle shading without problems.

Always case-by-case consideration... with around 35 modules (13kWp) at 60-80€ each (installed) one can consider a second or two smaller inverters ;)

With a roof occupied on 4 sides, this can indeed make sense "with or without" a second inverter and optimizers, since different roof sides can run in one string. The reason for the second inverter is otherwise that each side gets its own MPP and most inverters only have 2, the larger ones have 3.

Ok, I don’t understand much about it, but I take away that the solar installer didn’t talk absolute nonsense. It’s about 48 modules (18,~ kWp) on four roof sides (two long, two short) and he said that Solaredge would be quite practical, otherwise you would have to make a second inverter. He also said that with storage I would have to make a second inverter at full occupancy, so he only offered me full occupancy without storage or three-side occupancy with storage.

No, there have been completely different ones :D It will work.

Do you have larger shading? With shading, you can install these things, without it usually doesn’t make sense (min 2.5-3k€).

I would have all 4 sides equipped, 2 inverters for the opposite sides each, then they can even be chosen a bit smaller than the nominal power (the sun shines more on one side, north runs alongside).
Example:
1 inverter for north-south with 8-10kW, one string per roof side
1 inverter for east-west with 6-8kW, one string per roof side
one of the two inverters could also operate the storage as a hybrid.

I don’t know the pricing and product range for inverters at Solaredge, with Huawei the 10kW one would probably be 300-500€ cheaper than an 18kW, the 8kW would be about ~1500€ more, in return 3k€ less due to eliminated optimizers, small stuff like cables, GAK, fuses etc. would of course be added (estimated <1k€).

The last issue that could throw a wrench in the works would be too short string length on the short sides but all explainable.

I can sign almost anything, except this here:

2 inverters for the opposite sides,

is really only necessary if the roof sides are roughly different. If you find two roof sides with the same number of modules each, you connect them in parallel. Usually, this means North+South go in parallel to one MPPT, East+West as well. Depending a bit on the roof pitch, a 15 kW inverter should be sufficient for 18 kWp. That would be lean, less prone to errors, and efficient.